Question

A bus driver forgot to stop at a bus stop. Just as he passes the stop, he begins to decelerate 5 seconds later, the bus is 80m beyond the stop and has slowed to 10m/s.

a. Calculate the speed of the bus as it passed the bus stop.

b. What is the deceleration of the bus?

Answer 1

Solution;

when a body moves along a straight line with constant acceleration or deceleration,the equations of motion that describe the body's motion are:

$a=\frac{v_f-v_0}{t}$ ......(1)

Where ;

a is acceleration or deceleration.

v_f is the final velocity.

v₀ is the initial velocity.

t is the time taken.

The displacement in one direction would be;

$\Delta x=v_0t+\frac{at^2}{2}$ .....(2)

By substituting (1) into (2),Resolve to;

$\Delta x=\frac{v_f+v_0}{2}t$ ......(3)

Given;

$\Delta x=80m$

$v_f=10m/s$

$t=5s$

a)

Calculate speed of bus as it passed the stop;$v_0$ ;

Using equation (3),by direct substitution;

$80=\frac{10-v_0}{2}×5$

$32=10+v_0$

$v_0=32-10=22m/s$

Ans; 22m/s

(b)

Deceleration of the bus;

Using equation (1),by direct substitution;

$a=\frac{10-22}{5}$

$a=-2.4m/s^2$

(Negative shows the bus is decelerating)

Ans;2.4m/s²