Constant Velocity Motion Analysis

00:00 4 marks

A vehicle is traveling along a straight road with constant velocity. Its position at time t is described by a linear function.

(a) Write the expression for the velocity function of the vehicle.

(b) HL Extension: Given that the vehicle starts at position \(s(0)=50\) meters, find the displacement after \(t\) seconds.

Part a

3 minutes 2 marks

Question

State the velocity function for a vehicle moving with constant velocity. Assume the position function is linear of the form \(s(t) = ct + s_0\).

Hint Hint

Hint

Differentiate the linear position function \(s(t) = ct + s_0\) with respect to time \(t\) to find the velocity function.

Answer Answer
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Complete Answer

The velocity function is constant, i.e., \(v(t) = c\), where \(c\) is the constant velocity.

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Part b

3 minutes 2 marks

Question

Given that \(s(0)=50\) m, and knowing the velocity is constant, find the displacement of the vehicle after time \(t\). Express your answer in terms of \(c\) and \(t\).

Hint Hint

Hint

Displacement is the change in position from the initial position. For constant velocity, displacement is given by velocity multiplied by time.

Answer Answer
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Complete Answer

The displacement is \(\Delta s = c \times t\).

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