Question

show all work. include appropriate units and correct number of sig. figs in your answers. 2. a car travels at 12 m/s and speeds up uniformly over the next 6 seconds travelling 96 m during this time. a) find the acceleration. 2 marks b) find the velocity after 6 s. 2 marks

Explanation:

Step1: Use displacement - time formula

The displacement - time formula is $s = v_0t+\frac{1}{2}at^{2}$, where $s = 96\ m$, $v_0 = 12\ m/s$, $t = 6\ s$. Substitute these values into the formula: $96=12\times6+\frac{1}{2}a\times6^{2}$.

Step2: Solve for acceleration $a$

First, simplify the right - hand side of the equation: $12\times6+\frac{1}{2}a\times6^{2}=72 + 18a$. Then the equation becomes $96=72 + 18a$. Subtract 72 from both sides: $96 - 72=18a$, so $24 = 18a$. Solve for $a$: $a=\frac{24}{18}=\frac{4}{3}\approx1.33\ m/s^{2}$.

Step3: Use velocity - time formula for part b

The velocity - time formula is $v = v_0+at$. We know $v_0 = 12\ m/s$, $a=\frac{4}{3}\ m/s^{2}$, $t = 6\ s$. Substitute these values: $v=12+\frac{4}{3}\times6$.

Step4: Calculate the final velocity $v$

$v=12 + 8=20\ m/s$.

Answer:

a) The acceleration is $1.3\ m/s^{2}$ (2 sig. figs.).
b) The velocity after 6 s is $20\ m/s$ (2 sig. figs.).