Question

The acceleration of a cart started at t=0 varies with time as shown in figure. Find the distance traveled in 30 second and draw the position time graph.

Answer 1

Answer: Total Distance Travelled in 30sec = 1000 ft.

Explanation: In 1st 10 sec S1 = ut + 1/2 at^2

                                                 = 0 + 1/2 × 5 × 10^2

                                                 = 250 ft.

At 10 sec v = u + at

                   = 0 + 5 × 10

                   = 50 ft/sec

From 10 to 20 sec (Δt = 20 - 10 = 10sec) it moves with uniform velocity 50 ft/sec, distance S2 = 50 × 10

                                 = 500 ft.

Between 20 sec to 30 sec acceleration is constant i.e. -5 ft/s^2. At 20 sec velocity is 50 ft/sec.

t = 30 - 20

 = 10s

S3 = ut + 1/2 at^2

     = 50 × 10 + 1/2 (-5) (10)^2

     = 250 m.

Total distance travelled in 30 sec = S1 + S2 + S3

                                                        = 250 + 500 + 250

                                                        = 1000 ft.

                                                                ↑

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