# An object is moving with initial velocity of 20m/s. It must slow down to a stop in .33 seconds and travel 4m. Write a solution that applies a force to the object to satisfy the expected result.?

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The first thing I do not understand is why I can assume linear acceleration.

I have a basic understanding of calculus so explaining using integration is fine.

The first thing I do not understand is why I can assume linear acceleration.

I have a basic understanding of calculus so explaining using integration is fine.

##### 2 Answers

#### Explanation:

You may “assume” linear acceleration because you are asked for “a solution”, not *all* solutions.

F = m * a

d = v * t To stop in the specified distance and time.

4m = v(m/s) * 0.33s ; v = 12.12 m/s

To decelerate:

F = m * a

Applied force

#### Explanation:

Initial velocity

The applicable kinematic equation for a **constant acceleration** is

Let us find out for what time this retarding force is applied.

Using the other kinematic equation

we get

We see that the **object takes more time** than given in the question **to come to stop**. This implies that it is not a case of constant deceleration.

Let us assume that the object of mass

We know that acceleration can be written as

Using (1) and Integrating both sides we get

Suppose the force is given by the expression

Where

where

As

Expression becomes

We also know that velocity can be written in terms of displacement

Integrating both sides we get

Using (3) we get

Inserting given values in (3) and (4) we obtain

To solve for

Subtracting (7) from (6)

Inserting this value of

As such applied force