Motion in a Pla...

A point initially at rest moves along x-axis. Its acceleration varies with time as a = (6t + 5) in m/s². If it starts from origin, the distance covered in 2 seconds is

A bird flies for 4 s with a velocity of |t – 2|ms^–1 in a straight line, where t = time in seconds. It covers a distance of

A particle position as a function of time is described as x = 5 cos(2t + 1) What is the average velocity of the particle from t = 0 to t = 3s ?

A cyclist starts from place A and covers a distance of 2400 m to reach the place B. If the maximum possible acceleration of the cyclist is 2m/s² and its maximum retardation is 4m/s², what is the least time the cyclist can undertake the journey from A to B ?

A blind person after walking 10 steps in one direction each of length 80cm, turns randomly to the left or to right by 90º. After walking a total of 40 steps, the maximum displacement of the person from its starting point can be

An express train moving at 30 m/s reduces its speed to 10 m/s in a distance of 240 m. If the braking force is increased by 20% in the beginning, find the distance that it travels before coming to rest.

From the top of a tower of height 50m, a ball is thrown vertically upwards with a certain velocity. It hits the ground 10s after it is thrown up. How much time does it take to cover a distance AB where A and B are two points 20 m and 40 m below the edge of the tower ? (g = 10 ms^–2)

A point initially at rest moves along x axis. Its acceleration varies with time as a = (6t + 5) in ms^–2. If it starts from origin, the distance covered in 1 second is

The distance between two moving particles at any time is a. If ν be their relative velocity and ν₁ and ν₂ be the components of ν along and perpendicular to a the time when they are closest to each other is

A constant power P is applied to a particle of mass m. The distance travelled by the particle when its velocity increases from ν₁ to ν₂ is (neglect friction)