Question

When brakes are applied to a bus, the retardation produced is 25 $cm{s}^{-2}$ and the bus takes 20 s to stop.Calculate:(i) the initial velocity of bus,and (ii) the distance travelled by bus during this time.

Answer 1

Data given:
Retardation (-a) = - 25 cm/s²
Time taken to get stopped (t_av)=20 second
As the bus starts from rest,
∴ final velocity (v)= 0
Initial velocity (u)= ?
Distance(s) = ?
First we will calculate initial velocity of the bus.
We know
a = $\frac{(v-u)}{t}$
Or - 25 =$\frac{(0-u)}{20}$
Or -25 = -$\frac{u}{20}$
Or u = 25x 20
∴ u = 500 cm/s
Or u = (500/100) m/ s
Or u= 5 m/s

Again We know that:
s = ut + 1/2 a. t²
or S = 500x 20 + 1/2 $\times$(-25)$\times$ (20)²
or S = 10000 - 1/2 $\times$25$\times$ 400
or S = 10000 - 5000
or S = 5000 cm
or S = 50 m
∴ Initial velocity (u) = 5m/s and
Distance (s)=50m