**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:

**a)** Let u be the initial velocity of the body and v be the final velocity of the body. The body is accelerated uniformly with which is represented by a. The time taken is t. Therefore, the equation v = u + at.

Acceleration = change in velocity/time taken

a = (v-u)/t

at = v – u

v = u + at

**b)** Initial velocity, u = 54 km/h = 15 m/s

Final velocity, v = 0 m/s

Time, t = 8s

Acceleration, a = ?

a = (v-u)/t = -1.87 \mathrm{m/s^2}

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