Need Help with Linear and Angular Motion Homework?

[JohnP60]

Homework Statement

Need a bit off help with these questions would appreciate some help.

Homework Equations

1. An accelerating vehicle crosses a datum with a velocity of 20m/s and then covers a distance of 2.5km in 50s. Calculate the acceleration, and the velocity reached after it has traveled 2.5km.

2. If a rotor is rotating at 2000 rev/min accelerates to 3000 rev/min in 6 seconds calculate its acceleration and angle turned through.

3. Calculate the velocity of a belt in a belt drive system where the pulley is 82.3cm diameter and rotates at:
a) 1750 rev/min
b) 40 rev/s

The Attempt at a Solution

1. a=v-u / t
20/50 = 0.4m/s^2

v=u+at
20 + 0.4 x 50 = 40m/s

2. 314.16 - 209.43 / 6 = 17.5 rad/s^2

w= wo t + 1/2 a t^2
1256.58 + 315
= 1571.58 rad

3. Unsure how to do this one

Thanks

 

[mfb]

1. a=v-u / t
20/50 = 0.4m/s^2

This assumes the velocity changes by 20m/s in 50 seconds. You don't know if that is true.

v=u+at
20 + 0.4 x 50 = 40m/s

Simple cross-check: if the vehicle drives with a speed between 20m/s and 40m/s, in 50s it cannot go further than 40m/s*50s = 2km. Certainly not 2.5km.
Checks like those are useful to see if your answer can make sense.

314.16 - 209.43 / 6 = 17.5 rad/s^2

There are missing brackets, but this problem will vanish with proper fractions on paper.
I can confirm your answer.

3. The pulley is a circle, the belt is moving at the outer edge with the same speed as this outer edge.

 

[JohnP60]

Unsure what you mean with Q1. Am i using wrong formulas?

had a go at 3.

a)V=Rw
0.41x183.26
=75.14m/s

b)V=Rw
0.41x251.33
=103.04m/s

 

[mfb]

Unsure what you mean with Q1. Am i using wrong formulas?

Yes.

3 looks good.

As a general remark, it is easier to understand what you are doing if you start with a formula, and with the values given in the problem statement.