Question

A car accelerates from $18 \;km/h$ to $36 \;km/h$ in $10 \; sec$. Calculate the acceleration produced in the body.

Answer 1

Hint: -
Here the body is moving with some initial velocity and then in some passage of time its velocity changes to some new value, we need to find the acceleration produced in the body in the due time. Acceleration is defined as the rate of change of velocity.

Complete Step by Step Solution:
Initial velocity, u= 18 km/h
= \[18\times \dfrac{5}{18}=5m/s\]
Final velocity, v= 36 km/h
= \[36\times \dfrac{5}{18}=10m/s\]
Time taken, t= 10 s
Acceleration, $a$ = \[\dfrac{v-u}{t}=\dfrac{10-5}{10}=0.5m/{{s}^{2}}\]
So, the acceleration produced in the body is 0.5 \[m/{{s}^{2}}\]

Additional Information:
Since acceleration is defined as the rate of change of velocity and velocity itself is a vector quantity, so acceleration is also a vector quantity, so it can assume negative values also. A positive value of acceleration means the speed of the body is increasing while the negative value of acceleration means the velocity of the body is decreasing. Negative acceleration also termed as retardation. If a body moves with constant velocity then acceleration produced in the body is zero.

Note:
Sometimes we may get confused between acceleration and velocity. Acceleration can also be constant and in that case, the body changes its velocity at a constant rate. An object with negative acceleration can also speed up. If the acceleration points in the opposite direction of the velocity, the object will be slowing down. Also, using differentiation acceleration is the second derivative of position with respect to time.