(a)
The distance travelled by each car at various times.
(a)
Answer to Problem 5SP
The distances travelled by the car A at each consecutive seconds are
Explanation of Solution
Given info: Velocity of the car B is
Write the expression for distance.
Here,
Car A starts from rest. Hence, initial velocity is zero. Car B travels with constant velocity. Hence, its acceleration is zero.
For Car A,
Write the expression for distance.
At 1s,
Substitute 1s for t and
At 2s,
Substitute 2s for t and
At 3s,
Substitute 3s for t and
At 4s,
Substitute 4s for t and
For Car B,
Write the expression for distance.
At 1s,
Substitute 1s for t and
At 2s,
Substitute 2s for t and
At 3s,
Substitute 3s for t and
At 4s,
Substitute 4s for t and
Conclusion:
Therefore, the distances travelled by the car A at each consecutive seconds are
(b)
The time when Car A overtakes Car B.
(b)
Answer to Problem 5SP
Car A overtakes Car B between the interval
Explanation of Solution
Car A will overtake car B only when the distance travelled by car A becomes more than the distance travelled by car B. The result in part (a) shows that this does not happen till
Conclusion:
Car A overtakes Car B between the interval 3s and 4s.
(c)
The time at which car A overtakes car B.
(c)
Answer to Problem 5SP
The time at which car A overtakes car B is
Explanation of Solution
Given info: Velocity of the car B is
Equate the expressions for distances travelled by car A and car B.
Re-arrange the above equation to get t.
Substitute
Conclusion:
Therefore, the time at which car A overtakes car B is
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Chapter 2 Solutions
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