Question

A particle starting from rest moves with constant acceleration. If it takes 5.0 s to reach the speed 18.0 km/h find (a) the average velocity during this period, and (b) the distance travelled by the particle during this period.

Answer 1

Initial velocity of the particle, u = 0
Final velocity of the particle, v = 18 km/h = 5 m/s
Time, t = 5 s
Acceleration, a = (v − u)/t
⇒ a = (5 − 0)/5 = 1 m/s²
Distance, $s=ut+\frac{1}{2}a{t}^2$
$\Rightarrow s=\frac{1}{2}\times 1\times \left(5\times 5\right)=12.5\mathrm{m}$
(a) Average velocity, $v_{avg}=\frac{\mathrm{Total}\mathrm{displacement}}{\mathrm{Total}\mathrm{time}\mathrm{taken}}$
$\Rightarrow v_{avg}=\frac{\left(12.5\right)}{5}=2.5\mathrm{m}/\mathrm{s}$

(b) Distance travelled, s = 12.5 m