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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.

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Solution

(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:
Acceleration=Change in velocityTime taken
The above expression can also be written as,
a=v-ut
On further simplification, we get the 1st 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
(u) = 54 km/hr =54(1000)3600m/s =15 m/s
Final velocity (v) = 0 m/s
Time taken(t) = 8 s
So acceleration, a=v-ut
Put the values in the above equation to get the value of acceleration
a=0-158 =-1.875 m/s2

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