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Physics Chapter 3 : Topic 1
Equations of Motion
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The equations of motion are applicable only when:
Reasoning: The equations of motion are derived for uniformly accelerated motion where acceleration remains constant.
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In the equation $\mathbf{(v = u + at)}$, the symbol $\mathbf{(u)}$ represents:
Reasoning: $\mathbf{(u)}$ is the velocity at the beginning of motion.
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Two objects of different masses are dropped from the same height (ignoring air resistance). They:
Reasoning: Acceleration due to gravity is independent of mass.
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Which of the following represents the first equation of motion?
Reasoning: The first equation of motion relates final velocity, initial velocity, acceleration, and time.
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The SI unit of acceleration is:
Reasoning: Acceleration is the rate of change of velocity with time.
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A car starts from rest and accelerates at $\mathbf{5\ }\mathbf{m/s}^{\mathbf{2}}$. Its velocity after $\mathbf{4}$ seconds is:
Reasoning: $\mathbf{v = u + at}$ $\mathbf{\Longrightarrow}$ $\mathbf{v = 0 + (5)(4) = 20\ m/s}$
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A body moving with velocity $\mathbf{10\ m/s}$ accelerates at $\mathbf{2\ m/}\mathbf{s}^{\mathbf{2}}$ for $\mathbf{5}$ seconds. Final velocity is:
Reasoning: $\mathbf{v = u + at = 10 + (2)(5) = 20\ m/s}$
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A vehicle moving at $\mathbf{30\ m/s}$ stops in $\mathbf{6}$ seconds. Its acceleration is:
Reasoning: $\mathbf{a =}$ $\frac{\mathbf{v\ - \ u}}{\mathbf{t}}\mathbf{=}\frac{\mathbf{0\ - \ 30}}{\mathbf{6}}\mathbf{= - \ 5\ m/}\mathbf{s}^{\mathbf{2}}$ ; Negative sign shows retardation.
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A body starts from rest and travels $\mathbf{100\ m}$ in $\mathbf{5}$ seconds. Its acceleration is:
Reasoning: $\mathbf{s = ut +}$ $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{a}\mathbf{t}^{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{100 = 0 +}$ $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\times a \times 25}$ $\mathbf{\Longrightarrow}$ $\mathbf{a = 8\ m/}\mathbf{s}^{\mathbf{2}}$
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Which equation is most suitable when time is not given?
Reasoning: This equation does not contain time.
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A ball is thrown upward with velocity $\mathbf{20\ m/s}$. Taking $\mathbf{g = 10\ m/}\mathbf{s}^{\mathbf{2}}$, maximum height reached is:
Reasoning: At maximum height: $\mathbf{v = 0}$$\mathbf{v}^{\mathbf{2}}\mathbf{=}\mathbf{u}^{\mathbf{2}}\mathbf{- 2gh}$ $\mathbf{\Longrightarrow}$ $\mathbf{0 = 400 - 20h}$ $\mathbf{\Longrightarrow}$ $\mathbf{h = 20\ m}$
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In free fall without air resistance, acceleration of a body is:
Reasoning: All freely falling bodies accelerate downward with gravitational acceleration.
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The acceleration due to gravity near Earth's surface is approximately:
Reasoning: Standard value of gravitational acceleration is $\mathbf{9.8\ m/}\mathbf{s}^{\mathbf{2}}$.
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A body starts from rest. Its initial velocity is:
Reasoning: Starting from rest means initial velocity is zero.
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When a stone is thrown vertically upward, its acceleration:
Reasoning: Gravity always acts downward.
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At the highest point of upward motion, the velocity is:
Reasoning: The object momentarily stops before falling back.
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A freely falling object after $\mathbf{3}$ seconds has velocity $\mathbf{g = 10\ m/}\mathbf{s}^{\mathbf{2}}$:
Reasoning: $\mathbf{v = gt = 10}\left( \mathbf{3} \right)\mathbf{= 30\ m/s}$
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A stone dropped from rest falls $\mathbf{45\ m}$ in:
Reasoning: $\mathbf{s =}$ $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{g}\mathbf{t}^{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{45 = 5}\mathbf{t}^{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{t = 3s}$
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Projectile motion is an example of:
Reasoning: Projectile motion has both horizontal and vertical components.
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In projectile motion, horizontal acceleration is:
Reasoning: No horizontal force acts when air resistance is ignored.
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The vertical acceleration of a projectile is:
Reasoning: Gravity provides constant downward acceleration.
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The horizontal velocity of a projectile:
Reasoning: No horizontal acceleration acts.
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A projectile is launched at angle $\mathbf{45}^{\mathbf{o}}$. Its horizontal component of velocity is:
Reasoning: $\mathbf{u}_{\mathbf{x}}\mathbf{= u\ cos\ }\mathbf{45}^{\mathbf{o}}$ ; $\mathbf{u}_{\mathbf{y}}\mathbf{= u\ sin}\mathbf{45}^{\mathbf{o}}$ $\mathbf{\Longrightarrow}$ Both are equal.
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The horizontal component of initial velocity is:
Reasoning: Horizontal component uses cosine.
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The vertical component of initial velocity is:
Reasoning: Vertical component uses sine.
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At the highest point of projectile motion:
Reasoning: Only vertical velocity becomes zero temporarily.
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The path followed by a projectile is:
Reasoning: Combination of horizontal uniform and vertical accelerated motion produces a parabola.
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A projectile has maximum range when projected at:
Reasoning: Maximum range occurs at $\mathbf{45}^{\mathbf{o}}$ on level ground.
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If the initial velocity of a projectile is doubled, its range becomes:
Reasoning: $\mathbf{R \propto}\mathbf{u}^{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ Doubling velocity makes range four times.
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A projectile launched horizontally from a height has:
Reasoning: Gravity acts vertically downward.
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A ball thrown horizontally has initial vertical velocity:
Reasoning: Horizontal projection starts without vertical velocity.
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A projectile’s time of flight depends on:
Reasoning: Vertical motion determines time in air.
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When resolving projectile motion, the equations of motion are applied:
Reasoning: Horizontal and vertical motions are independent.
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A body moving with constant velocity has acceleration:
Reasoning: Acceleration is change in velocity; constant velocity means no change.
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If acceleration is negative, the body is:
Reasoning: Negative acceleration opposite to motion causes retardation.
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The slope of a velocity-time graph represents:
Reasoning: Gradient of velocity-time graph gives acceleration.
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The area under a velocity-time graph represents:
Reasoning: Area gives change in position.
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A freely falling body has increasing speed because:
Reasoning: Constant gravitational acceleration increases downward velocity.
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Two projectiles launched with the same speed at complementary angles have:
Reasoning: Angles $\mathbf{\theta}$ and $\mathbf{90}^{\mathbf{o}}\mathbf{- \theta}$ give equal range.
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The equations of motion cannot be used when:
Reasoning: Equations require uniform acceleration.
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