kinematic linear motion

A particle moves along a straight line and passes through a fixed point, O. The displacement, s meters, at time t seconds after the particle starts moving is given by s = 4 + 8t - t².

Calculate the instantaneous displacement in meters and determine the motion of the particle from the fixed point, O .

When t = 10

• 16 m to the left

• 16 m to the right

• 8 m to the right

• 4 m to the left

Answer explanation

just substitute t = 10 into the equation given

s = 4 + 8t - t²

s = 4 + 8(10) - (10)²

s = -16

thus, it moves 16 to the left

(negative sign shows that it moves to the left)

Choose the correct formula for velocity of a particle at time

• 
• 
• 
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Determine the velocity, v in terms of of t

(using the differentiation method)

s = 2t³ - 4t² + 2t + 1

• v = 6t² - 4t + 2

• v = 6t⁴ - 8t³ - 2t² + t

• v = 12t - 8

• v = 6t² - 8t + 2

Determine the v in terms of t

(differentiation)

s = t (2 - t)²

• v = 2 - t

• v = (2 − t)³

• v = 3t² - 8t + 4

• v = t (2t−1)

s = t(2t² − 9t − 5)

• v = 6t² - 18t - 5

• v = t² − 9t−5

• v = t (4t−9)

s = t³ (3 + t)²

• v = t² (6 + t)

• v = 6t² + t³

• v = 5t⁴ + 24t³ + 27t²