Question

(a) Derive the formula : v = u + at, where the symbols have usual meanings.
(b) A bus was moving with a speed of 54 km/h. On applying brakes it stopped in 8 seconds. Calculate the acceleration.

Answer 1

(a)
Consider a body has initial velocity (u) . Suppose it is subjected to a uniform acceleration (a) such that after time (t) its final velocity becomes (v). Now, from the definition of acceleration we know that:
$\mathrm{Acceleration}=\frac{\mathrm{Change}\mathrm{in}\mathrm{velocity}}{\mathrm{Time}\mathrm{taken}}$
The above expression can also be written as,
$a=\frac{v-u}{t}$
On further simplification, we get the 1^st equation of motion,
v = u + at
Where,
(a) - Acceleration
(v) - Final velocity
(u) - Initial velocity
(t) - Time taken

The equation v = u + at is called the first equation of motion and is used to calculate the velocity 'v' acquired by a body in time 't'.

(b) We have to find the value of uniform acceleration. So,
Initial velocity
$$\begin{gathered} \left(u\right)=54\mathrm{km}/\mathrm{hr} \\ =\frac{54\left(1000\right)}{3600}\mathrm{m}/\mathrm{s} \\ =15\mathrm{m}/\mathrm{s} \end{gathered}$$
Final velocity (v) = 0 m/s
Time taken(t) = 8 s
So acceleration, $a=\frac{v-u}{t}$
Put the values in the above equation to get the value of acceleration
$$\begin{gathered} a=\frac{0-15}{8} \\ =\boxed{-1.875m/s^2} \end{gathered}$$