Question

A body with initial velocity 5m/sec moves along a straight line with constant acceleration and travels 420 meters in 30 seconds. Calculate the average speed of the body during the time period (s), the final velocity of the body (V(subscript)f) and the acceleration on the body (a).
S=
V(sub)f=
a=​

Answer 1

Given :

Initial velocity = 5 m/s

Distance travelled = 420 m

Time of journey = 30 s

To Find :

Average speed, final velocity and acceleration of the body.

Solution :

★ Average speed is defined as the ratio of total distance travelled to the total time taken.

• It is a scalar quantity having only magnitude.
• SI unit : m/s

$\sf:\implies\:V_{av}=\dfrac{Total\:distance}{Total\:time}$

$\sf:\implies\:V_{av}=\dfrac{420}{30}$

$:\implies\:\underline{\boxed{\bf{\gray{V_{av}=14\:ms^{-1}}}}}$

★ Since body has constant acceleration throughout the journey, equation of kinematics can be applied to calculate acceleration and final velocity of the body.

1) Acceleration of the body :

$\sf:\implies\:d=ut+\dfrac{at^2}{2}$

$\sf:\implies\:420=(5)(30)+\dfrac{a(30)^2}{2}$

$\sf:\implies\:420=150+\dfrac{900a}{2}$

$\sf:\implies\:270\times2=900a$

$\sf:\implies\:a=\dfrac{540}{900}$

$:\implies\:\underline{\boxed{\bf{\orange{a=0.6\:ms^{-2}}}}}$

2) Final velocity of the body :

$\sf:\implies\:v=u+at$

$\sf:\implies\:v=5+(0.6)(30)$

$\sf:\implies\:v=5+18$

$:\implies\:\underline{\boxed{\bf{\purple{v=23\:ms^{-1}}}}}$