Question

Use the information below to answer the following 4 questions.

A 10.0-kg object is accelerated horizontally from rest to a velocity of 11.0 m/s in 5.00 s by a horizontal force.

1.The acceleration of the object is ___m/s². (Give your answer with 3 sig digs and do not include units).

2.The horizontal force given to the object is ___N. (Give your answer with 3 sig digs and do not include units).

3.The distance travelled by the object is ___m. (Give your answer with 3 sig digs and do not include units).

4.The work done on the object is ___J. (Give your answer with 3 sig digs and do not include units).

Answer 1

1.By defintion, the magnitude of the acceleration is given as follows:

$$a = \left| \dfrac{v_f - v_i}{t} \right|$$

where $t = 5s$ is the time taken by the object to thange its velocity from the initial one $v_i = 0$ to the final one $v_f = 11m/s$. Thus, obtain:

$$a = \dfrac{11m/s}{5s} = 2.20m/s^2$$

2. According to the second Newton's law, the force acting on the object is given as follows:

$$F = ma$$

where $m = 10kg$ is the mass of the object. Thus, have:

$$F = 10kg\cdot 2.2m/s^2 = 22.0N$$

3. The distance travelled by the object under the constant acceleration (and zero initial speed) is given by the kinematic equation:

$$d = \dfrac{at^2}{2} = \dfrac{2.2m/s^2\cdot (5s)^2}{2} = 27.5m$$

4. The work done on the object is given as follows:

$$W = Fd = 22.0N\cdot 27.5m = 605J$$

Answer. 1) 2.20, 2) 22.0, 3) 27.5, 4) 605.