Question

34.) 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

Answer:

a) Let the velocity of an object increase from u m/s to v m/s in time t

Then the rate of change of velocity with respect to time is given by

(v - u)/t. This quantity is called acceleration and given the symbol a

That is (v - u)/t = a

v - u = at ………..multiplying both sides by t

v = u + at ………….adding u to both sides

b) Initial Speed  (u)= 54 km /hr = 54 *1000 m / 3600 s = 54*5/18 = 15 m/s

        ( 1km = 1000 m and 1hr = 60 mins = 60*60 seconds = 3600 seconds)

       Time = 8 seconds

      Final Velocity (V) = 0

 we know that ,

        v = u + at

        0 = 15 + a*8

      0 = 15 + 8a

      a= -15/8 m/s²

  Therefore , acceleration is -15/8 m/s²

also ,

          S = ut+1/2at²

          S = 15*8² + 1/2 *(-15/8)*8²

             =15*64 - 15*4

            = 15(64 - 4)

            =15(60)

            S=900 m

hence Stopping Distance traveled before stopping is 900m .

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Answer 2

A)

$a = \frac{v - u}{t} \\ \\ a \times t \: = \: v - u \\ \\ v \: = u + at$

B) Speed = 54kmph

Speed = 54×5/18

Speed (u) = 15m/s

v =0ms (as bus stopped at end)

t = 8 sec

v = u+at

0 = 15 + a(8)

-15/8 = a

a = -1.89 m/s2