What is the power input at time t=3s for the force of 5N on an 8kg object?

AI Thread Summary
The discussion focuses on calculating the power input for an 8kg object subjected to a 5N force over time. Participants are attempting to derive the object's velocity as a function of time and express power as a function of time, particularly at t=3s. They also discuss a car's performance, needing to calculate the power developed by its engine and its speed after 4 seconds, assuming constant power. Key equations include relating power to work and kinetic energy, with emphasis on using acceleration to find velocity. The conversation highlights the importance of understanding how kinetic energy changes over time in relation to the force applied.
nns91
301
1

Homework Statement



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)

Homework 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 ??
 
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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.
 
2b. How can I know kinetic energy at 4s ? does the kinetic energy stay the same as in part a ??
 
nns91 said:
2b. How can I know kinetic energy at 4s ? does the kinetic energy stay the same as in part a ??
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.
 
Can I just calculate the acceleration and find velocity from there ?
 
Can I just calculate the acceleration and find velocity from there ?
 
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