Concept explainers
In each case, determine its velocity when t = 2 s if v = 0 when t = 0.
(a)
The velocity of the block when
Answer to Problem 1PP
The velocity of the block at the time
Explanation of Solution
Given:
The mass of the block is
Initially the velocity of the block is
The free body diagram of the block as shown in Figure (1a).
Write the formula for Newton’s second law of motion along
Here,
Write the formula for velocity of the block at constant acceleration as a function of time.
Here,
Conclusion:
Refer Figure (1a).
Resolve the forces along
Calculate the acceleration of the block.
Substitute
Calculate the velocity of the block at the time
Here,
Substitute
Thus, the velocity of the block at the time
b)
The velocity of the block when
Answer to Problem 1PP
The velocity of the block at the time
Explanation of Solution
Given:
The mass of the block is
Initially the velocity of the block is
The free body diagram of the block as shown in Figure (1b).
Write the formula for Newton’s second law of motion along
Here,
Write the formula for acceleration
Here,
Conclusion:
Refer Figure (1b).
Resolve the forces along
Calculate the acceleration of the block.
Substitute
Calculate the velocity of the block at the time
Here,
Substitute
Integrate at the limits of
Thus, the velocity of the block at the time
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