Question

34 n
the person experiences a reaction force of +34 n. what is the acceleration of the person?
remember: f = ma
58 kg
-0.68 m/s² +0.68 m/s²
+0.59 m/s² -0.59 m/s²

Explanation:

Step1: Recall the formula \( F = ma \)

We need to find acceleration \( a \), so rearrange the formula to \( a=\frac{F}{m} \).

Step2: Identify values of \( F \) and \( m \)

Given \( F = + 34\space N \) and \( m = 58\space kg \).

Step3: Substitute values into the formula

\( a=\frac{34}{58}\approx0.59\space m/s^{2} \)? Wait, no, wait. Wait, the force direction: Wait, the reaction force is +34 N, but let's check the diagram. The force arrow to the right is 34 N, but the person is pushing left? Wait, no, maybe I misread. Wait, the formula \( F = ma \), so \( a=\frac{F}{m} \). Let's calculate \( \frac{34}{58}\approx0.59 \)? Wait, no, 34 divided by 58: 34 ÷ 58 ≈ 0.586, which is approximately 0.59? Wait, but wait, the options: +0.59, -0.59, +0.68, -0.68. Wait, maybe I made a mistake. Wait, 34 divided by 58: 34/58 = 17/29 ≈ 0.586, which is approximately 0.59. But wait, the force direction: if the reaction force is +34 N, but maybe the actual net force is -34 N? Wait, the diagram: the black arrow is to the right (34 N), and the gray arrow is to the left (34 N)? Wait, no, the person is on a skateboard, pushing against a wall? Wait, the reaction force: when you push a wall, the wall pushes back. So if the person is pushing left, the wall pushes right with 34 N. So the force on the person is +34 N (right), mass 58 kg. Then acceleration \( a=\frac{F}{m}=\frac{34}{58}\approx0.59\space m/s^{2} \), positive because force is positive. Wait, but 34/58 is approximately 0.586, which rounds to 0.59. So the answer should be +0.59 m/s²? Wait, but let's recalculate: 34 divided by 58. Let's do 34 ÷ 58: 58 goes into 34 zero times. 58 goes into 340 five times (558=290), remainder 50. 58 goes into 500 eight times (858=464), remainder 36. 58 goes into 360 six times (6*58=348), remainder 12. So approximately 0.586, which is 0.59 when rounded to two decimal places. So the acceleration is \( + 0.59\space m/s^{2} \)? Wait, but wait, maybe I messed up the sign. Wait, if the force is to the right (+), then acceleration is to the right (+). So \( a=\frac{34}{58}\approx0.59\space m/s^{2} \), so +0.59 m/s².

Wait, but let's check the calculation again: 34 ÷ 58. Let's use a calculator: 34 ÷ 58 ≈ 0.5862, which is approximately 0.59. So the correct answer should be +0.59 m/s²? Wait, but the options have +0.59 and -0.59. So since the force is in the positive direction, acceleration is positive. So \( a = \frac{34}{58}\approx0.59\space m/s^{2} \), so +0.59 m/s².

Answer:

+0.59 m/s²