# Work and energy problem

1. Nov 15, 2008

### nns91

1. The problem statement, all variables and given/known data

1. A single force of 5N acts in the x direction on a 8kg object. (a) If the object starts from rest at x=0 at time t=-, find its velocity v as a function of time. (b) Write an expression for the power input as a function of time. (c) What is the power input of the force at time t=3s

2.A car manufacturer claims that his car can accelertate from frest to 100 km/h in 8s. The car's mass is 800kg.

(a) Assuming that this performance is achieved at constant power, determine the power developed by the car's engine.
(b) What is the car's speed after 4s (neglect friction and air resistance)

2. Relevant equations

p=W/t

3. The attempt at a solution[/b

1. I could not even do part a of number 1. Can you guys help me ?

2. So since it's constant power P=W/t. W can be calculated by 1/2 mv^2 right ?

How can I do part b ? Do I just use the P from previous calculation and multiply by time 4 s to get W. and set W=1/2 mv^2 ??

2. Nov 15, 2008

### phz

1a) F = ma gives you the acceleration, use it to find v(t).
1b) With 1a) you can get an expression for the work performed by the force on the object. Relate the work to the power and express p(t).
1c) Use 1b).

2a) You can express the cars kinetic energy at 100 km/h. This energy has been received linearly in time.
2b) You know the kinetic energy given after 4 s from 2a), relate it to velocity.

3. Nov 15, 2008

### nns91

2b. How can I know kinetic energy at 4s ? does the kinetic energy stay the same as in part a ??

4. Nov 15, 2008

### phz

Well, it differs in time, but it is given linearly according to the problem description, starting at 0 going up to the maximum value after 8 s. From 2a) you can express energy given per time unit which should give you energy given after 4 s.

5. Nov 15, 2008

### nns91

Can I just calculate the acceleration and find velocity from there ?

6. Nov 15, 2008

### nns91

Can I just calculate the acceleration and find velocity from there ?