Mechanics | Relativity Answers

1. An electric train accelerates uniformly from rest to a speed of 20 ms−1 which it maintains until the
brakes are applied. It is then brought to rest by a uniform retardation equal in magnitude to twice its
former acceleration. The total distance covered is 7.8 km and the total time taken is 7 minutes. Sketch a
velocity–time diagram. Calculate
(a) the time for which the train is travelling at constant speed,
(b) the initial acceleration in ms−2
.
2.A particle moves so that its position vector r at time t is
r = a cos ωt + b sin ωt,
where ω is a constant and a and b are constant vectors. Show that
(a) r · r˙ is independent of t,
(b) the acceleration is everywhere towards the origin and proportional to r.

plot the speed time graph from the table given below and calculate the distance covered by the particle during the time interval t=0 and t=0.4 sec. also find acceleration from the graph. choose appropriate scale

Calculate the kinetic energy of an object of mass 500g that is moving with a velocity of 20m/s

A machine part rotates at an angular speed of ωi. Its speed is then increased to ωf at an angular acceleration of α. If both the initial and final angular speeds are now doubled and the angular acceleration remains the same, by what factor is the angular displacement changed?

A machine part rotates at an angular speed of ωi. Its speed is then increased to ωf at an angular acceleration of α. If both the initial and final angular speeds are now doubled and the angular acceleration remains the same, by what factor is the angular displacement changed?

A machine part rotates at an angular speed of ωi. Its speed is then increased to ωf at an angular acceleration of α. If both the initial and final angular speeds are now doubled and the angular acceleration remains the same, by what factor is the angular displacement changed?

An object has a kinetic energy of 175 J and a momentum of magnitude 25.0 kg m/s. Find the speed of the object.

forces 5N, 12N and 13N acting on a body are in equilibrum. What is the angle between the forces 5N and 12N

2A bird of mass 0.6 kg stands on the midpoint of a horizontal rope. The rope sags and
angle of 150o is formed.
Find the tension in the rope.
Ans: T = 11.6 N

. A certain wire, 3 m long, stretches by 1.2 mm when under tension of 200 N. By how much does
an equally thick wire 6 m long, made of the same material and under the same tension, stretch?
A. 4.8 mm B. 2.4 mm C. 1.2 mm D. 0.6 mm