A point in a mechanism has an initial displacement of 1.3cm, and has a velocity given by𝑣(𝑡)=1.6𝑡+2,where 𝑡 is measured in seconds.1. Write an equation for the displacement 𝑠 at time 𝑡.

𝑎(𝑡)=8.7𝑡2+6,where 𝑡 is measured in seconds.1. Write an equation for the velocity 𝑣 at time 𝑡. Simplify your answer.𝑣(𝑡)=

The displacement of a particle is represented by the following equation : x = 3t3 + 7t2 + 5t + 8 where x is in metre and t in second. The acceleration of the particle at t = 1 is :-

The following ordinary differential equation describes the velocity of an object; velocity = x'(t)Write the expression for the displacement, x (in terms of t), if x = 1 when t = 0.Hints:Write an expression, not an equationTo type a2y𝑎2𝑦, use a^(2*y) in the answer box. Use ( ) while typing functions in the answer, for example cos(5x)𝑐𝑜𝑠(5𝑥).Check that the box is showing the answer and has identified the variables correctly

he displacement of a particle is givenby 𝑥 = (𝑡 − 2)2 where x is in meters andt in seconds. The distance covered bythe particle in first 4 seconds is

A particle moves along a straight line such that its displacement at any time t is given by S = t3 – 6t2 + 3t + 4 metres. The velocity when the acceleration is zero is :4 ms–1– 12 ms–1 42 ms–1– 9 ms–1