Question

How do you find the average acceleration given a car travels from rest in a distance of 400m in 16 seconds.

Answer 1

Hint: Now we are given the car is initially at rest hence we can say that the initial velocity was . Now we will find the final velocity of car by the formula $\text{speed=}\dfrac{\text{distance }}{\text{time}}$ . Now the rate of change of acceleration is given by $\dfrac{\text{change in velocity}}{\text{change in time}}$ . Hence we can find the average acceleration.

Complete step by step solution:
Now we know that acceleration is given by $\dfrac{\text{speed}}{\text{time}}$ .
Hence we have the average acceleration as $\dfrac{\text{change in velocity}}{\text{change in time}}$ .
Now let us first find the change in velocity.
Now initially the car was at rest hence the initial velocity was 0m per seconds.
Now let us first find the final velocity of the car.
Now we know that $\text{speed=}\dfrac{\text{distance }}{\text{time}}$ and the distance covered is 400m in 16 seconds.
Hence the final velocity is $\dfrac{400}{16}=25$m per seconds.
Hence change in velocity is 25 – 0 = 25 m per seconds.
Now the total time is again 16 seconds.
Hence average acceleration is $\dfrac{25}{16}=1.5625m/{{s}^{2}}$
Hence the average acceleration of the car is given by $1.5625m/{{s}^{2}}$

Note: Now note that here we have been asked about average change in acceleration. Remember that velocity is change in distance per unit time and acceleration is nothing but change in velocity per unit time. Hence to find acceleration we first need initial and final velocity.