A body cover a circular path of radius \(R\) in \(10Sec\). Calculate: the distance and displacement of the body at the end of \(30Sec\) and \(35Sec\).
Ans:(i) Total distance travelled \(=7\pi R\). (ii) Displacement \(2R\).
Calculate: the average speed of a man if he walks for \(1min\) at a speed of \(1 ms^{-1}\)and then runs for \(1min\) at a speed of \(3ms^{-1}\). Along a straight track?
Ans: \(2m.s^{-1}\).
A car covers \(\frac{1}{3}\) of the torak distance witha speed of \(30 kmh^{-1}\) and remaining distance with a speed of \(54 kmh^{-1}\). Find, the average speed of the car?
Ans: \(42.63km.h^{-1}\).
A car covers first half of total distance with a speed of \(54 kmh^{-1}\) and remaining distance with speed \(72 kmh^{-1}\). Find, the average speed of the car?
Ans: \(61.7km.h^{-1}\).
A body is moving in a straight line along X-axis. Its distance from the origin is given by equation, \(x=8t-t^{2}\). Where x is in meter and t is in second. Find, the average speed of the object in the time interval \(t=0\) and \(t=2s\). Calculate; its instantaneous speed at \(t=2s\).
Ans: \(v_{avg}=6m.s^{-1}\) and \(v_{t=2sec}=4m.s^{-1}\).
A boy runs from his home to the market \(2km\) away. He reaches the market in \(60min\). Seeing market closed, he at once runs back to his home and stops after \(30min\) at his friends house which is \(1km\) away from the market. Calculate: the average speed and magnitude of average velocity during the journey.
Ans: \(Speed_{avg}= 2km.h^{-1}\) and \(Velocity_{avg}=0.67km.h^{-1}\).
A body travels from point A to point B at \(40kmh^{-1}\)and from B to A at \(60kmh^{-1}\). Calculate: the average speed and average velocity.
Ans: \(Speed_{avg}=48km.h^{-1}\) and \(Velocity_{avg}=0\).
On a track of \(60km\), a train travels the first \(30km\) with the uniform speed of \(30kmh^{-1}\). How fast must the train travel in next \(30km\) so that the average speed will be \(40kmh^{-1}\) for the complete trip?
Ans: \(60km.h^{-1}\).
A body covers one-third of its journey with speed \(u\), next one-third with speed \(v\) and last one-third with speed \(w\). Calculate; the average speed of the body during the entire journey.
Ans: \(\frac{3uvw}{\left(uv+vw+wu\right)}\).
A car travels at a rate of \(20kmh^{-1}\) for \(10 min\) and then \(30kmh^{-1}\) for \(20min\). Calculate: (i) Total distance travelled by the car. and (ii)Average speed of the car during whole journey.
Ans:(i) \(d=13.33 km\) and (ii) \(Speed_{avg}=26.66km.h^{-1}\).
A man moves in a semi-circular track of radius \(40m\). If, he starts at one end of the track and reaches the other end, find the distance covered and displacement.
Ans: \(d=126m\) and \(\vec{S}=80m\).
A body moves in a straight line along X-axis, its displacement from the origin at any instant of time is given by; \(x=8t-3t^{2}\). (Here; X is in m,t is sec.)Calculate; (i)The average velocity in time interval \(t=0\) to \(t=2s\) (ii).Find, the instantaneous velocity of the body at the instant, \(t=0 \), \(t=2s\) and \(t=4s\).
Ans:(i) \(v_{avg}=2m.s^{-1}\) and (ii) \(v_{t=0}=8m.s^{-1}\), \(v_{t=2s}=-4m.s^{-1}\) and \(v_{t=4s}=-16m.s^{-1}\).
