(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.
(a) The consider a body having the initial velocity ‘u’.
Suppose it is subjected to a uniform acceleration ‘a’ so that after time ’t’ its final velocity becomes ‘v’.
Now, from the definition of acceleration we know that:
Acceleration = \(\frac{Change\;in\;velocity}{Time\;taken}\)
or Acceleration = \(\frac{Final\;velocity - Initial\;velocity}{Time\;taken}\)
So, a = \(\frac{v-u}{t}\)
at = v -u
and, v = u + at
where v = final velocity of the body
u = Initial velocity of the body
a = acceleration
and t = time taken
(b) Initial velocity, u = 54 km/h = 15 m/s
Final velocity, v = 0 m/s
Time, t = 8s
Acceleration, a = ?
a = \(\frac{v-u}{t}\) = \(\frac{0 -15}{8}\)
= \(\frac{-15}{8}m/s^2\) = -1.875 m/s2