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konstantin123 [22]

2 years ago

12

A driver moves with initial velocity of 40m/s accelerates uniformly at a rate of 12m/s2. It attains a velocity 52m/s. calculate

the distance covered during the journey.

1 answer:

r-ruslan [8.4K]2 years ago

5 0

Answer:

The total distance covered is 46m

Explanation:

From the question, we have the following given parameters.

Initial Velocity = 40m/s

Acceleration = 12m/s²

Final Velocity = 52m/s

Required

Calculate the distance covered during the journey

The question can be solved using the following equation of motion.

v² = u² + 2as

Where

v = final velocity = 52m/s

u = initial velocity = 40m/s

a = acceleration = 12m/s²

s = distance = ?

By substituting the above values in the stated formula

v² = u² + 2as becomes

52² = 40² + 2 * 12 * s

2704 = 1600 + 24s

Subtract 1600 from both sides

2704 - 1600 = 1600 - 1600 + 24s

1104 = 24s

Divide both sides by 24

1104/24 = 24s/24

46 = s

Reorder

s = 46

Hence, the total distance covered is 46m

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The amplitude in a simple harmonic motion corresponds to the maximum displacement of the mass-spring system. In this case, the mass is initially displaced by 0.4 m: this means that during its oscillation later, the displacement cannot be larger than this value (otherwise energy conservation would be violated). Therefore, this represents the maximum displacement of the mass-spring system, so it corresponds to the amplitude.

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$E=U=\frac{1}{2}kA^2$

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Equalizing the two expressions, we can solve to find A, the amplitude:

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