Physics Multiple Choice Questions on “Motion in a Straight Line – Acceleration”.
1. Which of the following is the correct formula for finding acceleration?
a) a = dx/dt
b) a = d2x/dt2
c) a = x/t
d) a = d3x/dt3
Answer: b
Clarification: Acceleration is the rate of change of velocity. Velocity is the rate of change of displacement. Therefore, acceleration is the rate of change of rate of change of displacement = d2x/dt2.
2. How does the displacement v/s time graph of a uniformly accelerated motion look like?
a) A straight line
b) A parabola
c) A hyperbola
d) An ellipse
Answer: b
Clarification: Here we use the second equation of motion. s = ut + (1/2)at2. In a uniformly accelerated motion, the acceleration remains constant. Therefore, the equation for displacement becomes the equation of a parabola.
3. The velocity of a body varies as, v = 2t+5t2. What is the acceleration at t = 10?
a) 102
b) 100
c) -100
d) 50
Answer: a
Clarification: Acceleration = dv/dt. To find the acceleration, we can differentiate the velocity equation with respect to time. a = 2 + 10t. On putting, t = 10, we get a = 102.
4. A ball falls from a building and covers 5m in 10s. What is the acceleration?
a) 0.1 m/s2
b) 0.2 m/s2
c) 9.81 m/s2
d) 10 m/s2
Answer: a
Clarification: Assuming the ball falls with zero initial velocity, then according to the second equation of motion, s = ut + (1/2)at2 = (1/2)at2. When we put t = 10s, we get a = 0.1 m/s2.
5. What is negative acceleration known as?
a) Deceleration
b) Acceleration
c) Escalation
d) Relaxation
Answer: a
Clarification: Negative acceleration is known is deceleration. Negative acceleration acts in the direction opposite to the direction of motion. It is also known as retardation.
6. A car is travelling in the north direction. To stop, it produces a deceleration of 60 m/s2. Which of the following is a correct representation for the deceleration?
a) 60 m/s2 Northwards
b) 60 m/s2 Southwards
c) 60 m/s2 Eastwards
d) 60 m/s2 Westwards
Answer: c
Clarification: Deceleration always acts in the direction opposite to the direction of motion. Magnitude of deceleration is 60 m/s2 and it acts in the direction opposite to North. Hence the answer is 60 m/s2 Southwards.
7. A uniformly accelerated body has ____
a) Constant speed
b) Constant velocity
c) Constant force
d) Constant momentum
Answer: c
Clarification: Since the body is accelerated, the speed and velocity will vary. Momentum depends on velocity; hence the momentum will also vary. The force remains constant as F = ma.
8. The velocity of a truck changes form 3 m/s to 5 m/s in 5s. What is the acceleration in m/s2?
a) 0.4
b) 0.5
c) 4.0
d) 5.0
Answer: b
Clarification: Acceleration is the rate of change of velocity. Here, the velocity changes form 3 m/s to 5 m/s in 5s. Hence, acceleration = (5-3)/5 = 0.4 m/s2.
9. The gradient of velocity v/s time graph is equal to____
a) Velocity
b) Acceleration
c) Distance
d) Momentum
Answer: a
Clarification: The gradient or slope of any graph tells us the value of its differential at that point. Since acceleration is the differential of velocity with respect to time, the gradient is equal to the acceleration.
10. The velocity of a ship varies with time as v = 5t3. What is the acceleration at t = 2?
a) 60
b) 56
c) 40
d) 100
Answer: a
Clarification: Acceleration of a body can be found out by differentiating the expression for velocity. Here v = 5t3. On differentiating, a = dv/dt = 15t2. On putting t = 2, we get a = 60 units.
11. If the velocity varies parabolically, how does the acceleration vary?
a) Linearly
b) Hyperbolically
c) Parabolically
d) Elliptically
Answer: a
Clarification: Velocity varies parabolically implies that velocity is of the form at + bt2. On differentiating the velocity, we get the equation for acceleration. Therefore, a = dv/dt = a+2bt, which is a linear equation. Hence the acceleration varies linearly.
12. The expression for displacement is x = sin(5t). The expression for acceleration is ______
a) 5sin(5t)
b) 25cos(5t)
c) -25sin(5t)
d) -5cost(5t)
Answer: a
Clarification: Acceleration = dv/dt = d2x/dt2. The velocity (v) can be expressed as, v = dx/dt = 5cos(5t). Hence acceleration (a) becomes, a = dv/dt = -25sin(5t).