Two objects are moving along the x axis. The position of object 1 is given by x = 5t2 + 4t + 2 (m/s). The acceleration of object 2 is given by a = -3t (m/s2) and its velocity is +15 m/s at 0s.
a. When do both objects have the same velocity?
b. Refer to (a), what is the velocity?
a. When do both objects have the same velocity?
b. Refer to (a), what is the velocity?
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obj 1: x = 5t² + 4t + 2
obj 1: dx/dt = V1 = 10t + 4
obj 2: a = -3t
obj 2: V2 = integral -3t = -3t²/2 + C
at t = 0 Vo = C = + 15 m/s
obj 2: V2 = -1.5t² + 15
V1 = V2 at t = ?
10t + 4 = -1.5t² + 15
0 = -1.5t² -10t + 11
solve quadratic for positive t value:
t = 0.961 s ANS a.
Vcommon = 10(0.961) + 4 = 13.6 m/s ANS b.
chk on ANS b.
Vcommon = -1.5t² + 15 = 13.61 m/s √
obj 1: dx/dt = V1 = 10t + 4
obj 2: a = -3t
obj 2: V2 = integral -3t = -3t²/2 + C
at t = 0 Vo = C = + 15 m/s
obj 2: V2 = -1.5t² + 15
V1 = V2 at t = ?
10t + 4 = -1.5t² + 15
0 = -1.5t² -10t + 11
solve quadratic for positive t value:
t = 0.961 s ANS a.
Vcommon = 10(0.961) + 4 = 13.6 m/s ANS b.
chk on ANS b.
Vcommon = -1.5t² + 15 = 13.61 m/s √