91Ó°ÊÓ

Acceleration is the rate at which an object changes its speed, measured in meters per second squared (\( \mathrm{m/s^2} \)). In this exercise, the race car accelerates from a standstill, and we assume the acceleration is constant. The kinematic equation used here is \( s = ut + \frac{1}{2}at^2 \), where:

• \( s \) is the distance covered (402 meters in this case).
• \( u \) is the initial velocity, zero since the car starts from rest.
• \( t \) is the time taken (6.4 seconds).
• \( a \) is the acceleration, which we need to find.

The equation simplifies to \( 402 = \frac{1}{2}a(6.4)^2 \). Solving for \( a \) involves rearranging the equation to find: \[a = \frac{2 \times 402}{(6.4)^2} \approx 19.64 \, \mathrm{m/s^2}\]This means the race car increases its speed by about 19.64 meters every second for every second it's accelerating.

Newton's second law of motion, which states that \( F = ma \), links the net force exerted on an object, its mass, and the resulting acceleration. This law is crucial for understanding how forces influence motion. In simple terms, the more force applied to an object, the faster it will accelerate, assuming mass is constant.For the race car, we apply Newton's second law to find the force the road must exert on the tires. Given the mass of the driver and car is 535 kg and the acceleration is previously calculated as 19.64 \( \mathrm{m/s^2} \), the force \( F \) is calculated as:\[F = 535 \times 19.64 \approx 10,509.4 \, \mathrm{N}\]This tells us that the road needs to push back on the tires with a force of approximately 10,509.4 newtons to maintain this acceleration. This force allows the car to gain speed efficiently.

Kinematic equations describe the motion of objects in terms of displacement, velocity, acceleration, and time, under the assumption of constant acceleration. They are essential tools in solving problems involving linear motion.In the problem, we used the kinematic equation \( s = ut + \frac{1}{2}at^2 \), suitable for objects starting with an initial velocity \( u \) and moving under constant acceleration \( a \). This set of equations helps determine unknown variables when others are known. Here:

• The initial velocity \( u \) was 0, because the car started from rest.
• The displacement \( s \) was given as 402 meters.
• The time \( t \) was 6.4 seconds.
• This allowed us to determine \( a \), the acceleration.

Understanding and applying kinematic equations compels us to break down motion into measurable factors, aiding in solving complex physics problems efficiently. They form a bridge between theoretical physics and practical observations.