Question

A particle moves in a straight line with a constant acceleration of 6.36 m/s^2 in the positive x direction. If its initial velocity is 2.33 m/s in the positive x direction, then how long, in seconds, does it take to move 7.34 m? t = __________________________________________ What is the particle’s final velocity in m/s?

Answer 1

The particle takes 1.22 seconds to move 7.34 m and its final velocity is 10.56 m/s.

Step-by-step explanation:

To find the time taken for the particle to move a distance of 7.34 m, we can use the equation of motion: s = ut + 0.5at^2, where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time. Plugging in the given values: 7.34 = 2.33t + 0.5(6.36)t^2. This is a quadratic equation, which can be solved to find the value of t.

By solving this quadratic equation, we find t = 1.22 seconds.

To find the final velocity, we can use the equation: v = u + at, where v is the final velocity. Plugging in the given values: v = 2.33 + (6.36)(1.22). Solving this equation gives us v = 10.56 m/s.

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