Need help with physics kinematics motorycle problem. Please explain your answer.

Question

Need help with physics kinematics motorycle problem. Please explain your answer. Thanks.

Two motorcycles are traveling along parallel straight paths with different velocities. Four seconds later, however, they have the same velocity. During this 4 second time interval, motorcycle A has maintained an average acceleration of 2 m/s2, whereas motorcycle B has maintained an average acceleration of 4 m/s2. You are also informed that motorcycle A has covered 1.2 times the distance of motorcycle B. From this information, calculate the initial velocities of both motorcycles.

Explanation / Answer

let initial velocity of motorcycle A is Va and initial velocity of motorcycle B is Vb.

so given is motorcycle A covered 1.2 times the distance of motercyle B. let motorcycle B covered d distance so motorcylce A covered 1.2d distance

now using equation

D = ut + 1/2*at^2

for motorcycle A

1.2d = Va*4 + (1/2)*2*4^2

1.2d = 4*Va + 16

Va = (1.2d - 16)/4 .... (1)

for motorcycle B

d = 4*Vb + (1/2)*4*4^2

d = 4*Vb + 32

Vb = (d - 32)/4.... (2)

and also final velocity is same for both.

using equation

v = u + at

for motorcycle A

V = Va + 2*4

V = (1.2d - 16)/4 + 8

and for motorcycle B

V = (d - 32)/4 + 4*4

so (1.2d - 16)/4 + 8 = (d - 32)/4 + 4*4

(1.2d - 16)/4 - (d - 32)/4 = 8

(1/4)*(1.2d - 16 - d + 32) = 8

0.2d + 16 = 32

d = 16/0.2 = 80 m

put in eq (1) and eq(2)

Va = (1.2*80 - 16)/4 = 20 m/s

Vb = (80 - 32)/4 = 12 m/s

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.