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

Replied by Admin
www.questionshouse.com/blog for daily updates and more answers...
 19 Mar 2019 @ 09:11

Replied by Admin
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
Hence, answer is 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) = (26333) / 42 = 230/2 = 115
Hence, answer is 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
Hence, answer is 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
Hence, answer is 72m/s
 10 Oct 2018 @ 09:46