# A particle's position moving an X axis is given by: X(t)= 4t³ + 3t - 5 , where X in meters ant t in seconds. 1- Find the particle's position at the following values of time (2s , 3s and 4s) ? 2- What is the particle's displacement between 2s and 4s ? 3- What is the average velocity between the time interval form t= 2s to t=4s ? 4- Find the instantaneous velocity at t=3s ? 5- Find the instantaneous acceleration at t=3s ?

• 19 Mar 2019 @ 09:11

A particle's position moving an X axis is given by: X(t)= 4t³ + 3t - 5 , where X in meters ant t in seconds.

1- Find the particle's position at the following values of time (2s , 3s and 4s) ?

(a) X(t)= 4t³ + 3t - 5 X(2)= 4×2³ + 3×2 - 5 = 32+ 6 - 5 = 33

(b) X(t)= 4t³ + 3t - 5 X(t)= 4× 3³ + 3×4 - 5 = 4×27 + 12 -5 = 112

(c) X(t)= 4t³ + 3t - 5 X(t)= 4×4³ + 3×4 - 5 = 256 +12 -5 = 263

Hence, answer for 2s , 3s and 4s is 33, 112, 263 respectively.

2- What is the particle's displacement between 2s and 4s ?

X (4) - X (2) = 263 -33 ( from the above answer) = 230

3- What is the average velocity between the time interval form t= 2s to t=4s ?

Average velocity = X (4)- X (2) / t (4)- t (2) = (263-33) / 4-2 = 230/2 = 115

4- Find the instantaneous velocity at t=3s ?

Instantaneous velocity V (X) = d x (t) /dt V (3) = d (4t³ + 3t - 5 )/ st = 4 dt³/dt + 3 dt/dt -5 d(0)/dt = 4 (3t2) +3 (1) -0 = 12×9+3 = 111

5- Find the instantaneous acceleration at t=3s ?

Instantaneous acceleration = d2x/ dt2 = d2 (4t³ + 3t - 5 )/ dt2 = 24×t +0 -0 = 24×3 = 72m/s

• 10 Oct 2018 @ 09:46