Acceleration and speed as m*s^-1

[Xecutive]

I was given this question today and I have never seen acceleration or speed with a minus power in the unit (m/s^-2). Also speed in the question has a ^-1 in the unit and I thought the unit for speed was m/s (meters per second)

Homework Statement

A body starts from rest and is subject to a constant contant acceleration of 4ms^-2 up to a speed of 20ms^-1. It then travels 20ms^-1 for 30 seconds after witch time it is retarded to a speed of 4ms^-1, if the complete motion takes 50 seconds, Find:

A) The time taken to reach 20ms^-1.

B) The retardation.

C)Total distance travelled.

Homework Equations

The Attempt at a Solution

I have know idea what these strange units mean.

 

[DrClaude]

Hi Xecutive. Welcome to PF!

It is simply standard algebra applied to units (which should be treated as mathematical objects).

$$x^{-1} = \frac{1}{x}$$

$$\mathrm{m} \; \mathrm{s}^{-1} = \frac{\mathrm{m}}{\mathrm{s}}$$

$$\mathrm{m} \; \mathrm{s}^{-2} = \frac{\mathrm{m}}{\mathrm{s}^2}$$

Note that it is not $\mathrm{m} / \mathrm{s}^{-1}$, but $\mathrm{m} \; \mathrm{s}^{-1}$. The former would give
$$
\mathrm{m} / \mathrm{s}^{-1} = \frac{\mathrm{m}}{\mathrm{s}^{-1}} = \mathrm{m} \; \mathrm{s}
$$

 

[PhanthomJay]

I was given this question today and I have never seen acceleration or speed with a minus power in the unit (m/s^-2).

you mean ms^-2 not m/s^-2

Also speed in the question has a ^-1 in the unit and I thought the unit for speed was m/s (meters per second)

yes, the unit for speed is m/s, and m/s can be written as ms^-1...it's just taking the denominator, s, and placing it in the numerator as s^-1.
I personally would rather see it written as m/s instead of ms^-1, but they are nevertheless mathematically the same unit, just an algebraic manipulation of the variables.

Welcome to these forums!

 

[Xecutive]

It seems so obvious now.

Thanks.

 

[HalfLostAndSearching]

Hello,

I understand your confusion about the units given in this question. It is important to note that the units for acceleration and speed can be expressed in different ways, and both m*s^-1 and m/s^-2 are valid units for acceleration, while m/s and m/s^2 are valid units for speed.

In this context, m*s^-1 is most likely being used as a shorthand for m/s^-2, which is the standard unit for acceleration. This means that the body is experiencing an acceleration of 4 meters per second per second (m/s^2) or 4 meters per second squared.

Similarly, m/s^-1 is most likely being used as a shorthand for m/s, which is the standard unit for speed. This means that the body is traveling at a speed of 20 meters per second (m/s) or 20 meters per second.

To answer the given questions, we can use the equations of motion:

A) The time taken to reach 20m/s can be found using the equation v = u + at, where v is the final velocity, u is the initial velocity (which is 0 in this case), a is the acceleration, and t is the time. Plugging in the values, we get: 20 = 0 + 4*t. Solving for t, we get t = 5 seconds.

B) The retardation can be found using the equation v = u + at, where v is the final velocity (which is 4 m/s in this case), u is the initial velocity (which is 20 m/s), a is the retardation, and t is the time (which is 30 seconds). Plugging in the values, we get: 4 = 20 + a*30. Solving for a, we get a = -0.5333 m/s^2.

C) The total distance traveled can be found using the equation s = ut + 1/2at^2, where s is the total distance traveled, u is the initial velocity (which is 0), a is the acceleration (which is 4 m/s^2), and t is the total time taken (which is 50 seconds). We can also break this into two parts: the distance traveled while accelerating and the distance traveled while decelerating.

Distance traveled while accelerating: s = 0 + 1/2*4*5^2 = 50