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# Category Archives: KINEMATICS

## Time Dilation problem – Special Relativity

With what speed will a clock have to be moving in order to run at a rate that is one half the rate of a clock at rest?

Posted by Mona

Using the formula for Relativistic Time (according to Special Theory of Relativity)

$T=\frac{T_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$

√[1 – (v²/c²)] = ½ → v² = (3/4)c²

v = [√3/2]*c = .866c

## Angle between acceleration and velocity in projectile motion

What is the angle between the directions of  acceleration and velocity at the highest point of projectile?

At the highest point of a projectile, the vertical component of velocity is zero and the velocity is entirely horizontal. The direction of acceleration (due to gravity) is vertically downwards throughout the motion of the projectile.

Therefore, the angle between the direction of acceleration and velocity at the highest point of a projectile is 90 °

## The problem of a rock thrown vertically up

A rock is thrown vertically upward from the ground with an initial speed 15m/s.

a. how high does it go
b. how much time is required for the rock to reach its maximum height?
c. what is the rock’s height at t=2.00s?

(Posted by Merhawi)

(a)

u=15m/s

a=-10m/s2

v=0 m/s (at the max height)

S=?

v2-u2=2aS

S=v2-u2/2a

=225/20

=11.25 m

(b) From the above case

using v=u+at

t=v-u/a=1.5s

(c) Use S = ut + 1/2 at2

put t=2s, u = 15m/s, a=-10m/s2

S=30 – 20 = 10 m

(If you use g = 9.8 m/s2 The answers will be slightly different)

## Equations of Motion – Images for easy reuse

Here you can find the equations of motion in the form of images which you can use in your documents.

$v = u + at$ $S = ut + \frac{1}{2} at^{2}$ $v^{2} = u^{2} + 2aS$

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