Question 2.4: THE DAYTONA 500 GOAL Apply the basic kinematic equations. PR...
THE DAYTONA 500
GOAL Apply the basic kinematic equations.
PROBLEM A race car starting from rest accelerates at a constant rate of 5.00 \mathrm{~m} / \mathrm{s}^{2}. (a) What is the velocity of the car after it has traveled 1.00 \times 10^{2} \mathrm{ft} ? (b) How much time has elapsed? (c) Calculate the average velocity two different ways.
STRATEGY We’ve read the problem, drawn the diagram in Figure 2.16, and chosen a coordinate system (steps 1 and 2). We’d like to find the velocity v after a certain known displacement \Delta x. The acceleration a is also known, as is the initial velocity v_{0} (step 3, labeling, is complete), so the third equation in Table 2.4 looks most useful for solving part (a). Given the velocity, the first equation in Table 2.4
| Table 2.4 equations for Motion in a straight Line Under Constant Acceleration | |
| Equation | Information Given by Equation |
| v = v_0 + at | Velocity as a function of time |
| \Delta_x = v_0 t + \frac{1}{2}at^2 | Displacement as a function of time |
| v^2 = v_0^2 + 2a\Delta x | Velocity as a function of displacement |
| Note: Motion is along the x– axis. At t = 0, the velocity of the particle is v_0. | |
can then be used to find the time in part (b). Part (c) requires substitution into Equations 2.2
\bar{v} ≡ \frac{Δx}{Δt} = \frac{x_f – x_i}{t_f – t_i} [2.2]
and 2.7,
\bar{v} ≡ \frac{v_0 + v}{2} (for constant α) [2.7]
respectively.
