Acceleration Problems and Solutions

 Problem #1

A car travelling at 20 ms^-1 takes a U-turn in 20 s without changing its speed. What is the average acceleration of the car?

Answer:
Initial velocity v_i = + 20 ms^-2, final velocity v_f = –20 ms^-2.
Average acceleration = change in velocity/time taken
                                 = (v_f – v_i)/t
Average acceleration = (–20 – 20)/20 =  –2 ms^-2
Negative sign indicates that average acceleration is towards left during the time interval given.

Problem #2
A car drives in a straight line at a constant speed of 70 km per hour for 9 seconds. Find its acceleration.

Answer:
Since the car's velocity is constant, there is no acceleration. So, a = 0.

Problem #3
A remote control car is driven along a straight track at 4 m/s. The child controlling the car then activates the toy's turbo mode so that, 2 seconds later, the car's speed is 6 m/s. Find its average acceleration.

Answer:
Given: initial velocity v_i = 4 m/s, final velocity v_f = 6 m/s, time interval Δt = 2 s,
So, average acceleration is
a_avg = (v_f – v_i)/Δt = (6 – 4)/2 = 1,0 m/s²

Problem #4
Shortly after, the remote control car in the previous example exits turbo mode, slowing from 6 m/s back to 3 m/s in 3 seconds. Find the car's average acceleration over this interval.

Answer:
Given: initial velocity v_i = 6 m/s, final velocity v_f = 3 m/s, time interval Δt = 3 s,
So, average acceleration is
a_avg = (v_f – v_i)/Δt = (3 – 6)/3 = –1,0 m/s²
Note that the acceleration is negative because the car slowed down while moving in the positive direction, meaning the acceleration effectively occured in the direction opposite to the velocity.

Problem #5
A plane has a take off speed of 400 km/h. What is the acceleration in m/s² of the plane if the plane started from rest and took 50 seconds to take off?

Answer:
given: initial velocity v_i = 0 (from rest) and the final velocity v_f = 400 km/h (take off). Hence
So, average acceleration is
a_avg = (v_f – v_i)/Δt
       = (0 – 400 km/h)/50 s = –8 km/jam/s
a_avg = –2.22 m.s^-2

Problem #6
Starting with a constant velocity of 60 km/h, a car accelerates for 15 seconds at an acceleration of 1.0 m/s² . What is the velocity of the car at the end of the period of 15 seconds of acceleration?

Answer;
given: initial velocity v_i = 60 km/h = 1,67 ms^-1, acceleration a = 1,0 m.s^-2, time t = 15 s,
From average acceleration
a_avg = (v_f – v_i)/Δt
The above equation gives the equation
1,0 = (v_f – 1.67)/15
v_f = 16.67 ms^-1 or
v_f = 16.67 x 3600 x (1 : 1000) kmh^-1 = 60.0 km.h^-1

Problem #7
How long does it take to accelerate a car from a speed of 60 km/h to a speed of 110 km/h at an acceleration of 2 m.s^-2?

Answer:
Given: The initial velocity v_i = 60 km/h = 16.67 ms^-1 and the final velocity v_f = 110 km/h = 30.56 ms^-1 and we are given the acceleration a = 2 ms^-2.
 From average acceleration
a_avg = (v_f – v_i)/Δt
2.0 = (30.56 – 16.67)/Δt
The above equation gives the equation
2Δt  = 13.89
Δt = 6.94 s or   

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