Dynamics with Variable Acceleration

00:00 6 marks

An object is moving along a straight line and its acceleration depends on its velocity. The acceleration is given by \(a(t)=4-0.2v(t)\), where \(v(t)\) is the velocity. The object has an initial velocity of 5 m/s. Answer the following parts:

Part a

3 minutes 2 marks

Question

Set up the differential equation that relates the acceleration \(a(t)\) to the velocity \(v(t)\) of the object.

Hint Hint

Hint

Recall that acceleration is the time derivative of velocity.

Answer Answer
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Complete Answer

The differential equation is \(\frac{dv}{dt} = 4 – 0.2v\).

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Part b

5 minutes 4 marks

Question

Solve the differential equation \(\frac{dv}{dt} = 4 – 0.2v\) to find the velocity function \(v(t)\), given that \(v(0)=5\) m/s.

Hint Hint

Hint

Use separation of variables or the integrating factor method.

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Complete Answer

\(v(t)=20-15e^{-0.2t}\)

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