State Newton's first law of motion - Leaving Cert Physics - Question 6 - 2011

The forces acting on the car before it hit the tree include:

• Gravity (mg) acting downwards.
• Normal reaction force from the ground acting upwards.
• Friction (drag force) acting opposite to the direction of travel (left to right).
• Engine force acting in the direction of travel (right to left).
• Brakes also put a resistance on the car.

To calculate the acceleration, we use the formula:

$a = \frac{v - u}{t}$ Where:

• $u = 15$ m s⁻¹ (initial velocity)
• $v = 0$ m s⁻¹ (final velocity)
• $t = 0.4$ s

Substituting the values:

$a = \frac{0 - 15}{0.4} = -37.5 \, \text{m s}^{-2}$

Thus, the acceleration is $-37.5 \, \text{m s}^{-2}$, showing a deceleration.

Using Newton's second law:

$F_{net} = m \cdot a$ Where:

• $m = 1400$ kg
• $a = -37.5 \, \text{m s}^{-2}$

Calculating:

$F_{net} = 1400 \cdot (-37.5) = -52500 \, \text{N}$

The net force acting on the car during the collision is $-52500 \, \text{N}$.

Kinetic energy (KE) can be calculated using the formula:

$KE = \frac{1}{2} m v^2$

Substituting in our values:

$KE = \frac{1}{2} \cdot 1400 \cdot (15^2) = 157500 \, \text{J}$

Thus, the kinetic energy of the moving car before impact was $157500 \, \text{J}$.

The kinetic energy of the moving car was converted to potential energy as it struck the tree and also transformed into heat and sound energy due to the collision.

According to Newton's first law, objects in motion tend to stay in motion unless acted upon by an unbalanced force. During a collision, a back seat passenger can continue moving forward due to inertia, potentially causing injury to themselves or others.

This risk of injury is minimized by wearing a seatbelt, which applies an external force that counters the passenger's inertia, keeping them restrained during the collision.