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4. A 1.7 t car is accelerated at 1.7 m/s2 for 11 s on a horizontal surface. If the initial velocity was 33 km/h and the force due to friction on the road surface was 0.5 N/kg, determine force applied in the same direction as motion.

5. Immediately after reaching its final velocity, the car in question (4) breaks and comes to a stop in 7 m. Determine the breaking force acting on the car.

User Claudioz
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4) First, we need to convert the initial velocity from km/h to m/s:

33 km/h = 9.17 m/s

Next, we can use the formula for acceleration:

a = (v_f - v_i) / t

where a is the acceleration, v_f is the final velocity, v_i is the initial velocity, and t is the time.

Substituting the given values, we get:

1.7 m/s^2 = (v_f - 9.17 m/s) / 11 s

Solving for v_f, we get:

v_f = 28.97 m/s

Next, we can use the formula for force:

F = m * a

where F is the net force, m is the mass of the car, and a is the acceleration.

Substituting the given values, we get:

F = 1.7 t * 1.7 m/s^2

F = 2.89 kN

Finally, we need to account for the force due to friction on the road surface. The force due to friction is given by:

f_friction = friction coefficient * m * g

where friction coefficient is the coefficient of friction between the car's tires and the road surface, m is the mass of the car, and g is the acceleration due to gravity (9.81 m/s^2).

Substituting the given values, we get:

f_friction = 0.5 N/kg * 1.7 t * 9.81 m/s^2

f_friction = 8.35 kN

Since the force due to friction acts in the opposite direction to the motion of the car, we need to subtract it from the net force to get the force applied in the same direction as motion:

F_applied = F - f_friction

F_applied = 2.89 kN - 8.35 kN

F_applied = -5.46 kN

The negative sign indicates that the force applied is in the opposite direction to the motion of the car. Therefore, the force applied in the same direction as motion is 5.46 kN.

5) To determine the braking force acting on the car, we can use the formula:

F = m * a

where F is the net force acting on the car, m is the mass of the car, and a is the deceleration of the car due to braking.

First, we need to find the final velocity of the car. We can use the formula:

v_f^2 = v_i^2 + 2ad

where v_f is the final velocity, v_i is the initial velocity (which is equal to the velocity of the car when it reaches its final velocity), a is the acceleration (which is equal to the deceleration due to braking), and d is the distance over which the car comes to a stop.

Substituting the given values, we get:

v_f^2 = 28.97 m/s^2 + 2(-a)(7 m)

Since the car comes to a stop, the final velocity is 0. Solving for a, we get:

a = 28.97 m/s^2 / 14 m

a = 2.07 m/s^2

Now we can use the formula for force to find the braking force:

F = 1.7 t * 2.07 m/s^2

F = 3.519 kN

Therefore, the braking force acting on the car is 3.519 kN.

User Khamitimur
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User Matthew Coelho
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