Question

A bike rider pedals with constant acceleration to reach a velocity of 7.8 m/s over a time of 4.2 s. during the period of acceleration, the bike's displacement is 19 m. what was the initial velocity of the bike?

Answer 1

To calculate the initial velocity of the bike, we use the following equation

$d=\frac{1}{2} (u+v)t$.

or

$u=\frac{2d}{t} -v$

Here, u is initial velocity, v is final velocity, t is the time and d is the distance covered by bike.

Given, $u =7.8 m/s$,$d= 19 m$ and $t=4.2 s$.

Substituting these values in above equation, we get

$u = \frac{2 \times 19}{4.2 \ s} -7.8 m/s = 9.05 \ m/s - 7.8 \ m/s \\\\ u= 1.2 m/s$.

Thus, the initial velocity of the bike is 1.2 m/s.