Question

The displacement of a particle along the X-axis is given as
x=5t2+1
, where x is in metres and t in seconds. Calculate its average velocity in the time interval between 2 s and 3 s.
21 m/s
40 m/s
46 m/s
25 m/s

Answer 1

Answer on Question #51860, Physics, Mechanics, Kinematics, Dynamics

Question:

The displacement of a particle along the X-axis is given as

$$x = 5t^2 + 1$$

where $x$ is in metres and $t$ in seconds. Calculate its average velocity in the time interval between 2 s and 3 s.

21 m/s

40 m/s

46 m/s

25 m/s

Answer:

Velocity of the particle equals:

$$v = \frac{dx}{dt} = \frac{d}{dt} (5t^2 + 1) = 10t$$

Average velocity in the time interval between 2 s and 3 s equals:

$$v_a = \frac{\int_{t_1}^{t_2} v \, dt}{t_2 - t_1} = \frac{\int_{2}^{3} 10t \, dt}{3 - 2} = 5 \cdot 3^2 - 5 \cdot 2^2 = 25 \frac{m}{s}$$

Answer: $25 \frac{m}{s}$

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