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A roller coasters velocity at the top of the hill is $10\frac{m}{s}$ . Two seconds later it reaches the bottom of the hill with a velocity of $26\frac{m}{s}$ . What is the acceleration of the coaster? $\newline$ A. $18\frac{m}{s^{2}}$ $\newline$ B. $10\frac{m}{s^{2}}$ $\newline$ C. $8\frac{m}{s^{2}}$ $\newline$ D. $32\frac{m}{s^{2}}$

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Relate position, velocity, speed, and acceleration using derivatives

Full solution

Q. A roller coasters velocity at the top of the hill is

10\frac{m}{s}

. Two seconds later it reaches the bottom of the hill with a velocity of

26\frac{m}{s}

. What is the acceleration of the coaster?

\newline

A.

18\frac{m}{s^{2}}

\newline

B.

10\frac{m}{s^{2}}

\newline

C.

8\frac{m}{s^{2}}

\newline

D.

32\frac{m}{s^{2}}

Identify Velocities and Time: Identify the initial velocity $v_i$ , final velocity $v_f$ , and the time $t$ it takes to change from the initial to the final velocity. $\newline$ Initial velocity $v_i = 10$ m/s $\newline$ Final velocity $v_f = 26$ m/s $\newline$ Time $t = 2$ seconds
Use Acceleration Formula: Use the formula for acceleration $a$ , which is the change in velocity $\Delta v$ divided by the time $\Delta t$ during which the change occurred. $\newline$ Acceleration $a$ = (Final velocity - Initial velocity) / Time $\newline$ $a = \frac{v_f - v_i}{t}$
Calculate Acceleration: Plug in the known values into the acceleration formula to calculate the acceleration. $\newline$ $a = \frac{26 \, \text{m/s} - 10 \, \text{m/s}}{2 \, \text{s}}$ $\newline$ $a = \frac{16 \, \text{m/s}}{2 \, \text{s}}$ $\newline$ $a = 8 \, \text{m/s}^2$

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