A particle moving along x-axis has acceleration f, at time t, given by f = f0 (1-t/T), where f0 and T are constants…

Q: A particle moving along x-axis has acceleration f, at time t, given by f = f_0 (1-\frac{t}{T}) , where f0 and T are constants. The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0, the particle’s velocity (vx) is

(a) f0T

(b) (1/2) f0T2

(c) f0T2

(d) (1/2) f0T

Ans: (d)
Sol: Putting f = 0

\displaystyle f_0(1-\frac{t}{T}) = 0

Hence , t = T

\displaystyle \int_{0}^{v}dv = \int_{0}^{T}f dt

\displaystyle v = \int_{0}^{T}f_0(1-\frac{t}{T}) dt

A bus is moving with a speed of 10 ms–1 on a straight road. A scooterist wishes to overtake the bus in 100 s…

Q: A bus is moving with a speed of 10 ms–1 on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus?

(a) 20 ms–1

(b) 40 ms–1

(c) 25 ms–1

(d) 10 ms–1

Ans: (a)

Sol:Let speed of scooterist = v

Distance traveled by bus in 100 s is
= 10 x 100 = 1000 m

To overtake the bus , distance traveled by scooterist = 1000 + 1000 = 2000m

To overtake ,

2000 = 100 v

v = 20 m/s