Driving into a wall moving at 30 mph is how many times harder than driving into the wall at 15 mph?

When considering the impact force in a collision, it is important to look at the relationship between speed and kinetic energy. Kinetic energy is calculated using the formula ( KE = \frac{1}{2}mv^2 ), where ( m ) represents mass and ( v ) is the velocity.

At 15 mph, if you calculate the kinetic energy, it would be proportional to ( (15)^2 ), which equals 225. When driving into a wall at 30 mph, the kinetic energy is proportional to ( (30)^2 ), which equals 900.

To find out how many times harder the impact is when driving at 30 mph compared to 15 mph, you can take the kinetic energy at 30 mph and divide it by the kinetic energy at 15 mph. So, ( 900 \div 225 = 4 ).

Therefore, driving into a wall at 30 mph is 4 times harder than driving into the wall at 15 mph, which is why this option is correct. Understanding this principle highlights the significant increase in kinetic energy and thus impact force as speed increases.