Question

A bus accelerates at 2 metre per second square for the first 10 seconds after the start and retards at 1 m per second square for next 10 seconds find the total distance

Answer 1

Let the time it had acceleration a1=2m/s2a1=2m/s2 be tt. Distance s1s1 travelled is at22=2t22=t2at22=2t22=t2.

Now, time with acceleration a2=−1m/s2a2=−1m/s2 will be 20−t20−t. Here, u2=a1t=2tu2=a1t=2t. Distance s2s2 travelled is ut+at22=2t2−(20−t)22=4t2−400−t2+40t2ut+at22=2t2−(20−t)22=4t2−400−t2+40t2.

Total distance s=s1+s2=5t2−400+40t2

Answer 2

acceleration = 2m/s^2 for first 10 sec
initial velocity = 0 as from start(rest)
final velocity = 4m/sec^2
acceleration = 1m/s^2 for next 10 sec
initial velocity = 4m/s^2
final velocity = 2m/s^2
distance = sped × time
= 2×20
= 40m