Motion in A Str...

A cart is released from rest at the top of a long ramp at time $$t = 0$$ seconds and moves down the ramp at a constant acceleration rate. At a time of t, the cart has reached a speed of $$2 m/s$$. How fast will the cart be moving at the time of $$3t$$?

A 10 kg object free-falling from a cliff. Find out the velocity of the object after 1 sec and after 2 sec?

A cat running with constant acceleration in one direction is at rest initially and has velocity $$v\left(t\right)=1.00{m}/{s}$$ at $$2.00$$ seconds later.
At $$t=4.00$$ seconds, how far away from the starting point will the cat be?

A driver applies brakes when he sees a child on the railway track, the speed of the train reduces from 54 km $$h^{-1}$$ to 18 km $$h^{-1}$$ in 5 s. What is the distance travelled by the train during this interval of time?

A particular rocket is propelled in one direction such that its acceleration as a function of time is expressed by $$a\left(t\right)=A{t}^{2}+B$$ where $$A$$ and $$B$$ are constants.
The position function of the rocket should depend on which power of $$t$$?

A $$50.0\ kg$$ boy is sitting on an amusement park ride where he accelerates straight upward from rest to a speed of $$30.0 m/s$$ in $$3.0 s$$
What is his mass as he accelerates upward?

Two trains depart from one station, one going north at $$30.00$$ miles per hour, and another going west, steadily accelerating with a rate of $$0.3333$$ miles per minute.
How many minutes after departure would the two trains be $$50.00$$ miles apart?

At an airport, a bored child starts to walk backwards on a moving platform. The child accelerates relative to the platform with $$a=-0.5{m}/{{s}^{2}}$$ relative to the platform.
The platform moves with a constant speed $$v=+1.0{m}/{s}$$ relative to the stationary floor.
In $$4.0$$ seconds, how much will the child have been displaced relative to the floor?

The length of a minute hand of a clock is 4 cm. Find the displacement and average velocity of the tip of the minute hand when it moves during a time interval from
(a) 3: 15 pm to 3 : 30 pm(b) 4: 15 pm to 4: 45 pm.

An insect moves along the sides of a wall of dimensions 12 m x 5 m starting from one corner and reaches the diagonally opposite corner. If the insect takes 2 s for its motion then find the ratio of average speed to average velocity of insect.