Question

A particle moves according to the equation x=2t^2-5t+6.Find i) average velocity in the last 3 sec ii)Velocity at t=3s.
a) 1 m/s, 7 m/s b) 4 m/s,3 m/s c)2 m/s, 5 m/s d)3 m/s, 7 m/s

Answer 1

Answer on Question #52075, Physics, Mechanics | Kinematics | Dynamics

A particle moves according to the equation $x=2t^2-5t+6$.

Find i) average velocity in the last 3 sec ii) Velocity at t=3s.

a) $1 \mathrm{~m} / \mathrm{s}, 7 \mathrm{~m} / \mathrm{s}$ b) $4 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}$ c) $2 \mathrm{~m} / \mathrm{s}, 5 \mathrm{~m} / \mathrm{s}$ d) $3 \mathrm{~m} / \mathrm{s}, 7 \mathrm{~m} / \mathrm{s}$

Solution:

i) Average velocity

$$v_{av} = \frac{\Delta x}{\Delta t} = \frac{x(3) - x(0)}{3 - 0} = \frac{9 - 6}{3} = 1 \mathrm{~m/s}$$

ii) Velocity is

$$v = \frac{dx}{dt} = 4t - 5$$

Velocity at $t=3s$

$$v(3) = 4 * 3 - 5 = 7 \mathrm{~m/s}$$

Answer: a) $1 \mathrm{~m/s}, 7 \mathrm{~m/s}$

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