# Kinematics of rectilinear motion - multiple displacements

• derRoboter
In summary, the problem involves a cheetah and an antelope starting at rest and accelerating to their maximum speeds in 4 seconds. The cheetah catches the antelope in 15 seconds and the distance between them at the start is 126m. Equations for constant acceleration, including v=u+at, s=ut+1/2at^2, v^2=u^2+2as, and s=1/2(u+v)t, are provided to help solve the problem.
derRoboter

## Homework Statement

A cheetah is estimated to be able to run at a maximum speed of $$100km.h^1$$ whilst and antelope can run at a maximum speed of $$65km.h^-1$$. A cheetah at rest sees an antelope at rest and starts running towards it. The antelope immediately starts running away. Both cheetah and antelope are assumed to move with constant acceleration and reach their maximum speeds in 4 seconds. Assuming that both run along the same straight line and that the cheetah catches the antelope in 15 seconds, find the distance between the animals when they first started moving. 2. Equations I have been given
$$v=u+at$$
$$s=ut+1/2at^2$$
$$v^2=u^2+2as$$
$$s=1/2(u+v)t$$misc

I have been staring at this for a good hour now and am yet to come up with the answer which I know to be 126m. How do i find this value using those equations and the data given?

Kind regards, derRoboter

Last edited:
anyone?

## 1. What is rectilinear motion?

Rectilinear motion refers to the motion of an object along a straight line with a constant speed or velocity. This type of motion is also known as linear motion.

## 2. How is displacement calculated in rectilinear motion?

Displacement in rectilinear motion can be calculated by taking the difference between the final position and the initial position of the object. It is a vector quantity and is represented by the symbol 'd'.

## 3. What is the difference between displacement and distance in rectilinear motion?

Displacement is the shortest distance between the initial and final position of an object, while distance is the total length of the path traveled by the object. Displacement is a vector quantity, while distance is a scalar quantity.

## 4. What is the difference between speed and velocity in rectilinear motion?

Speed is the rate of change of distance, while velocity is the rate of change of displacement. Speed is a scalar quantity, while velocity is a vector quantity that includes both magnitude and direction.

## 5. How do multiple displacements affect the overall displacement in rectilinear motion?

In rectilinear motion, multiple displacements can be added together to find the overall displacement of an object. This is known as the principle of superposition, where the net displacement is equal to the sum of all individual displacements.

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