At t = 0, one toy car is set rolling on a straight track with initial position 1

Question

At t = 0, one toy car is set rolling on a straight track with initial position 17.0 cm, initial velocity -2.8 cm/s, and constant acceleration 3.00 cm/s2. At the same moment, another toy car is set rolling on an adjacent track with initial position 9.5 cm, initial velocity 5.20 cm/s, and constant zero acceleration.

(a) At what time, if any, do the two cars have equal speeds? (Enter NA if the cars never have equal speeds.) s

(b) What are their speeds at that time? (Enter NA if the cars never have equal speeds.) cm/s

(c) At what time(s), if any, do the cars pass each other? (If there is only one time, enter NA in the second blank. If there are two times, enter the smaller time first. If they never pass, enter NA in both blanks.) s s

(d) What are their locations at that time? (If there is only one position, enter NA in the second blank. If there are two positions, enter the smaller position first. If they never pass, enter NA in both blanks.) cm cm

(e) Explain the difference between question (a) and question (c) as clearly as possible.

Explanation / Answer

x1 = 17cm ; u1 = -2.8cm/s ; a1 = 3cm/s2

x2 = 9.5cm ; u2= 5.2cm/s ; a2 = 0

a ) let t =t both have same speed

as their is no acceleration in car 2 so at t= t speed of car 1 = 5.2cm/s

5.2 = -2.8 + 3t

b) t = 8/3 sec when both car have speed = 5.2cm/s

c) Let Distance travelled by car 2 = X at time = t

distance travelled by car 1 = X - 9.5

for car 2: X = 5.2t

for car 1: X -9.5 = -2.8t + 1.5t2

5.2t - 9.5 =  -2.8t + 1.5t2

8t = 1.5t2 + 9.5

t = 3.54sec and t 1.78 sec

d) Location at both t

X = 5.2t = 18.4m (at t = 3.54 sec)

X = 5.2t = 9.25m (at t =1.78sec)

for a) both car are different location but are having same speed

c) different speed and at same location

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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